Why Do People Trust Bitcoin?

Unlike centralized fiat payment systems, Bitcoin is fully open-source and decentralized.Transactions can be verified independently at any time. Bitcoin payments can be made instantly and directly without an intermediary.

The whole system is protected by a combination of elliptic curve cryptography and hashing on the sha256 curve. Together these mechanisms sufficiently provide large enough random key-space that cannot be attacked by hackers or gamed through mathematics.